Hong Life CalculatorsUnderstanding the reserve ratio calculator — concept and principle
The reserve ratio is the share of customer deposits a bank holds as reserves, either as vault cash or in its account at the central bank. This calculator compares a bank's reserves with the required amount, finds its excess reserves and shows the maximum deposit expansion in the textbook model.
How it is calculated
- Reserve ratio = reserves ÷ deposits.
- Required reserves = deposits × required ratio.
- Excess reserves = reserves − required reserves (the amount the bank could lend now).
- Simple money multiplier = 1 ÷ required ratio.
- Maximum deposit expansion = excess reserves × multiplier.
The principle
Banks do not keep all deposits in the vault; they lend most of them out. When a loan is spent, the money is deposited in another bank, which keeps a fraction and lends the rest. If every bank keeps exactly the required fraction and lends everything else, the total new deposits form a geometric series equal to the excess reserves × 1 ÷ required ratio. Cash kept outside banks and reserves held voluntarily make the real expansion smaller. With a 0% requirement, as in the US since March 2020, the multiplier is not defined and lending is limited by capital rules and loan demand instead.
Worked example
Default inputs: deposits 10,000,000 USD, reserves 1,500,000 USD, required ratio 10%.
- Reserve ratio = 1,500,000 ÷ 10,000,000 = 15%.
- Required reserves = 10,000,000 × 10% = 1,000,000 USD.
- Excess reserves = 1,500,000 − 1,000,000 = 500,000 USD: above the requirement; the bank could lend 500,000 USD now.
- Simple multiplier = 1 ÷ 0.10 = 10.
- Maximum deposit expansion = 500,000 × 10 = 5,000,000 USD.
| Customer deposits | Reserve ratio (reserves ÷ deposits) |
|---|---|
| 2.5e+06 | 60% |
| 5e+06 | 30% |
| 7.5e+06 | 20% |
| 1e+07 | 15% |
| 1.25e+07 | 12% |
| 1.5e+07 | 10% |
| 2e+07 | 7.5% |
How to read the result
A reserve ratio above the requirement means the bank has room to lend. In practice, modern banks are constrained more by capital and liquidity rules (such as the Basel III liquidity coverage ratio) and by demand for loans than by reserve requirements. The maximum expansion is an upper bound under textbook assumptions, not a forecast.
Common mistakes
- Treating the simple multiplier as how money is created in practice.
- Forgetting that cash holdings by the public reduce the expansion.
- Confusing reserve requirements with capital requirements.
- Using a 0% requirement and expecting a finite simple multiplier.
Frequently asked questions
What is the reserve requirement in the US?
The Federal Reserve reduced reserve requirement ratios to 0% in March 2020.
What are excess reserves?
Reserves above the required amount, which a bank can lend or hold.
Do banks lend out reserves?
Banks create deposits when they lend; reserves settle payments between banks. The textbook model is a simplification of that process.
Sources: Board of Governors of the Federal Reserve System, Reserve Requirements · Mishkin, F. S., The Economics of Money, Banking and Financial Markets (multiple deposit creation)